You say that 2/(29+13*sqrt(5)) = 1/29. Basically an irrational number = a rational number. That is nonsense.
You haven't mentioned how you obtain your "Hugo" number for a given prime index. For example, how did you get Hugo(31) = 169746333457? Please explain the algorithm.
You haven't mentioned how you test/prove a "Hugo" number prime. Please explain the algorithm and its runtime complexity.
Finally, you're comparing the n'th "Hugo" prime to n'th Mersenne prime. That is meaningless. In fact, it merely shows that "Hugo" primes are rarer than Mersenne primes. That's actually a bad thing.
A class of numbers is suitable for prime finding if there is a fast algorithm for proving them and they have higher than average probability (compared to normal numbers of same size) of being prime. You have not discussed either of these aspects.
Last fiddled with by axn on 20210124 at 13:05
